Discrete and Weyl density of states for photonic dispersion relation

• Published in: Physica scripta Vol. 94; no. 10; pp. 105001 - 105006
• Main Authors: Aydin, Alhun, Oikonomou, Thomas, Bagci, G Baris, Sisman, Altug
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.10.2019
• Subjects: confined systems; density of states; Fysik med inriktning mot atom- molekyl- och kondenserande materiens fysik; Physics with spec. in Atomic, Molecular and Condensed Matter Physics; Weyl's conjecture
• ISSN: 0031-8949; 1402-4896; 1402-4896
• DOI: 10.1088/1402-4896/ab0bc5

The current density of states (DOS) calculations do not take into account the essential discreteness of the state space, since they rely on the unbounded continuum approximation. Recently, discrete DOS based on the quantum-mechanically allowable minimum-energy interval has been introduced for the quadratic dispersion relation. In this work, we consider systems exhibiting a photonic (photon-like) dispersion relation and calculate the related density and number of states (NOS). Also, a Weyl's conjecture-based DOS function is calculated for photons and acoustic phonons at a low-frequency limit, by considering the bounded continuum approach. We show that the discrete DOS function reduces to expressions of bounded and unbounded continua in the appropriate limits. The fluctuations in discrete DOS completely disappear under accumulation operators. It is interesting that relative errors of NOS and DOS functions with respect to discrete ones have exactly the same character as the ones of the quadratic dispersion relation. Furthermore, the application of discrete and Weyl DOS for the calculation of internal energy of a photon gas is presented and the importance of discrete DOS is discussed. It is shown that the discrete DOS function given in this work needs to be used whenever the low energy levels of a physical system are heavily occupied.